We demonstrate a three-dimensional (3D) monolithic micro-actuator fabricated by non-ablative femtosecond laser micromachining and subsequent chemical etching. The actuating principle is based on dielectrophoresis. An analytical modeling of this actuation scheme is conducted, which is capable of performance prediction, parameter optimization and instability analysis. Static and dynamic characterizations are experimentally verified. An actuation range of 30 mu m is well attainable; resonances are captured with an evaluated quality factor of 40 (measured in air) and a bandwidth of 5 Hz for the primary vertical resonance of 200 Hz. A settling time of 200 ms in transient response indicates the damping properties of such actuation scheme. This actuation principle suppresses the need for electrodes on the mobile, non-conductive component and is particularly interesting for moving transparent elements. Thanks to the flexibility of the manufacturing process, it can be coupled to other functionalities within monolithic transparent micro-electro-mechanical systems (MEMS) for applications like tunable optical couplers.